A1 3.9 Check Your Understanding

Front

What is the minimum number of batches a baker needs to make at least 150 cookies if each batch makes 12 cookies?

Back

To find the minimum number of batches, divide the total cookies needed by the number of cookies per batch: \( \frac{150}{12} = 12.5 \). Since the baker cannot make half a batch, round up to 13 batches.

Front

If a car rental company charges a flat fee of $50 plus $0.20 per mile driven, what is the maximum number of miles a customer can drive with a budget of $100?

Back

The total cost is \( 50 + 0.20x \leq 100 \). Solving for \( x \): \( 0.20x \leq 50 \) leads to \( x \leq 250 \) miles.

Front

What inequality represents the requirement that children must be 80 pounds or more to ride in the front seat in Virginia?

Back

The inequality is \( c \geq 80 \), meaning a child's weight (c) must be greater than or equal to 80 pounds.

Front

If a school has a total cost limit of $500 for a field trip and charges $25 per student, what is the maximum number of students that can attend?

Back

The total cost is \( 25x \leq 500 \). Solving for \( x \): \( x \leq 20 \) students.

Front

A factory produces at least 500 units of a product each day. If each machine produces 25 units per hour, what is the minimum number of hours the machines need to operate each day?

Back

To find the minimum hours, divide the total units by the units produced per hour: \( \frac{500}{25} = 20 \). Therefore, the machines need to operate for at least 20 hours.

Front

What is an inequality?

Back

An inequality is a mathematical statement that shows the relationship between two expressions that are not equal, using symbols like <, >, ≤, or ≥.

Front

How do you solve an inequality?

Back

To solve an inequality, isolate the variable on one side using similar steps as solving an equation, but remember to reverse the inequality sign when multiplying or dividing by a negative number.

Front

What does the symbol '≥' mean?

Back

'≥' means 'greater than or equal to', indicating that the value on the left is either greater than or equal to the value on the right.

Front

What does the symbol '≤' mean?

Back

'≤' means 'less than or equal to', indicating that the value on the left is either less than or equal to the value on the right.

Front

What is a linear inequality?

Back

A linear inequality is an inequality that involves a linear expression, which can be written in the form ax + b < c, ax + b > c, etc.